Foundation of Advanced Mathematics (II). 2

Author: Brouer
Publisher:
Publish Date: 2006-01-01
Features: This is the second volume of the textbook "Fundamentals of Advanced Mathematics" written by the same authors. It includes vector algebra and analytic geometry in space, multivariable calculus, and linear ordinary differential equations. The intentions and features are as introduced in the preface to the first volume. We repeat the important advice to students in the first volume, as it is equally important for this second volume. In order to learn calculus, it is not enough to read the textbook as if it were a newspaper. Learning requires careful reading, working through examples step by step, and solving problems. Solving problems requires more than imitation of examples. It is necessary to think about what the problem really asks and to develop a method for that particular problem. If something is still not clear after you have tried to understand it, you should ask a classmate, a more advanced student, or your teacher. If a classmate asks you a question, you may learn a great deal from explaining the answer. The following two additional remarks might be helpful to readers in using the second volume. (1) The material online about systems of ordinary differential equations (section 9.2) is not included in the fundamental requirements. Before studying it, readers will need some basic knowledge of linear algebra. (2) Some of the material in this volume has been stated in terms of matrices and determinants. For readers who are not yet familiar with the basic concepts and operations of matrices and determinants, we have included a brief outline in Appendix A.